4. Recall, the set of functions from a set A to a set B is denoted...

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4. Recall, the set of functions from a set A to a set B is denoted by BA. (a) Consider the set S = {a, b, c} and design a bijection between NS (the set of all functions from {a, b, c} to N) and the set N N N. On the other hand design a bijection between SN and [0, 1]. (b) Design a bijection between ({0, 1} N) N and {0,1} NXN (c) Prove that the set of all sequences of real numbers has cardinality c. (Hint: one such sequence is a function from N to [0, 1]) 4. Recall, the set of functions from a set A to a set B is denoted by BA. (a) Consider the set S = {a, b, c} and design a bijection between NS (the set of all functions from {a, b, c} to N) and the set N N N. On the other hand design a bijection between SN and [0, 1]. (b) Design a bijection between ({0, 1} N) N and {0,1} NXN (c) Prove that the set of all sequences of real numbers has cardinality c. (Hint: one such sequence is a function from N to [0, 1])